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	<h1 class="heading-1" style="font-size:34px;text-align:center">DNA Origami of Taj Mahal</h1>
	<!-- <p style="margin:-10px 0 20px 0;font-size:13px;font-style:italic;text-align:center;">Manish K. Gupta, Mayank Kandpal and Avinash Parida</p>  -->



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		<h2 style="padding:0px 0 10px 0;">Abstract</h2>
		<p>The research on the constructions of 3D origami is attracting many researchers to explore the possibility for making useful tools as well as novel structures. In particular, in April 2011 Hao Yan group has demonstrated curved surfaces using 3D DNA origami. Motivated by this work in this project we aim to develop highly complex non-trivial 3D structure of Taj Mahal using two different construction techniques – Single-shape DNA origami and Multi-shape DNA origami. This will involve new algorithms and software development. We have identified the basic building blocks of Taj Mahal namely Decagonal Dome (29nm radius, 10 crossovers, 8 rings), Cylindrical Tubes (10nm radius tubular), Pyramidal Tops (13nm radius, 5 crossovers, 5 rings), Cubical Body (85nm width) and square base. Combining these basic shapes is still a challenge in Multi-shape DNA origami and experimental validation for the same is needed.  We also report interactive software KonCAD focusing on prototyping, rendering and analyzing structural details of DNA origami structures with complex curvatures. Prior to this work, we have also created the 2D structures of the map of India and Gujarat state. Currently, we utilize tools like caDNAno, Nano Engineer and Autodesk Maya.</p>
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	<div class="mag-content">
		
	
		
		
		
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		<li> 
			<article>
				<header>
				<h1><a name="introduction">Key-words</a></h1>
				<p class="infos"></p> 
				</header>
				<p>Taj Mahal, DNA origami, 3D, 2D, KonCAD, M13 virus, caDNAno</p>
			</article>
		</li>


			<li> 
				<article>
					<header>
					<h1><a name="introduction">1. Introduction</a></h1>
					<p class="infos"></p> 
					</header>
					<p>Paul Rothemund while working at Caltech came up with a remarkable idea in 2006. He extended the self assembly of DNA to another dimension by folding the DNA of a M13 virus (the virus that infects the bacteria) to various interesting shapes such as smiley face, star, map of north America etc by using another set of DNA helper strands that work as staples (using the Watson and Crick base paring) on the viral DNA [17], [18]. Rothemund called it DNA origami. Origami as we know is a Japanese art of paper folding so is DNA origami as an art of DNA folding into desired shape. In order to fold the DNA Paul wrote computer programs to determine the appropriate DNA staples for a given shape. This field has been extended into many directions such as 3D DNA origami and to DNA Kirigami. Kirgami is an extension of origami where we also allow the cutting together with simply folding.</p><br/>
					<p>After the breakthrough work by Rothemund [18], where he constructed many 2D structures to demonstrate the proof of principle of DNA origami many researchers attempted to create several interesting and useful tools and objects out of DNA origami. In [16], map of china was created by Lulu et al. In 2009 DNA origami was used to construct ruler by Friednich Simmel [10] to measure distance between single molecules. In the same year William Shih’s team constructed many nanoscale tools (toothed gears, bent rods etc.) [4,11] and Paul Rothemund in collaboration with IBM reported his early work on nanoscale circuitry [14]. At the same time in the year 2009, Kurt Gothelf et al [2], constructed 3D box at nanoscale with a lid. This was a major step in the 3D DNA origami as previously only nanotubes were constructed. It is predicted that this can be used to carry drug molecule. In early 2010; Hao Yan and Yan Liu have shown how to use ’tiles’ instated of ’single strand staples’ to create DNA origami structures. This technique allowed scaling up the nanoscale structures by 4 times [22]. The potential applications are in creating nano-bread board for assembling nanoscale circuits. In Oct 2010; Hao Yan went one step further in creating a nanoscale Mobius strip [8]. This has given birth to DNA kirigami. His group is also working on artificial leaf project [20] where the group wants to create an artificial photo system-II with the help of DNA origami that can provide hydrogen fuel from water in an artificial photosynthesis experiment. The reader is referred to further papers for more information [3,15,1,19,13,9].</p><br/>
					<p>Motivated by the DNA origami of curved surfaces in this work we consider the DNA origami of Taj Mahal. The Taj Mahal is the marvel of design engineering. It was built by Mughal Emperor Shah Jahan about 350 years ago at Agra, India using more than 22,000 workers, millions of dollars and 22 years of time span [23]. This turns out to be one of the wonders of the world. Building the Taj Mahal using DNA origami at the nano-scale is also a challenging problem from nano technology perspective. We adopted two design techniques to construct the 3D Taj Mahal. The first designing technique of Taj Mahal, single-shape DNA origami, is similar to that proposed by Castro et al [3] where they demonstrated how to design and produce an object shaped like a robot using 3D DNA origami, and uses caDNAno as the CAD software. Our structure is packed on a honeycomb lattice. We tried to maintain various kinds of stability in the structure using available designing principles proposed by different researches. The second technique we worked on is Multi-shape DNA origami. It is quite challenging and tries to combine various different 3D structures to form one big 3D structure, with a solid 3D base holding all the parts together. We have identified and designed the basic building blocks of Taj Mahal namely Decagonal Dome (29nm radius, 10 crossovers, 8 rings), Cylindrical Tubes (10nm radius tubular), Pyramidal Tops (13nm radius, 5 crossovers, 5 rings), Cubical Body (85nm width) and square base. The designing was done using Nano Engineers and Autodesk Maya. We propose multiple techniques to combine these shapes. However, these techniques still require experimental validation, and thus combining these basic shapes is still an open challenge. We also present software, KonCAD, which is aimed at speeding up the initial designing and prototyping process while creating multiple curved DNA origami structures of varying sizes. The rendered design uses the designing principles that we studied in our background readings, so the end users would get the output as a structure, which completely obeys all the designing principles. Currently we have developed a 2D version of the software for creating rings and squares. In future we hope to extend it to 3D so that all the basic shapes of Taj Mahal can be created easily.</p><br/>
					<p>This wiki is organized as follows. Section 2 provides an overview of 3D origami of curved structures. Section 3 discusses the single shaped (strand) and multi shaped (strands) DNA origami methods. Section 4 discusses results obtained and some general discussions on proposed solutions. Section 5 describes software KonCAD which helps in 2D origami of structures of varying size for squares and rings. Finally Section 6 concludes the wiki. </p><br/>					
				</article>
			</li>


		<li> 
			<article>
				<header>
				<h1><a name="background">2. Origami of Curved Structures in 3D:</a></h1>
				<p class="infos"></p> 
				</header>
				<p>3D DNA origami has been achieved using different construction techniques. There are techniques for creating hollow container-like objects by folding up single layers of helices [25,2,27]. Hao Yan group  have also  presented a strategy to design and construct self-assembling DNA Nanostructures, which form 3D curved shapes. Also, it is possible to create space-filled structures using a multi-layered approach [26,4,28,18], though the yield is less and takes longer. One can either use a square lattice or a honeycomb lattice for building space-filled multi-layered structures. There also exist a few techniques to join two specific kinds of 3D structures. For space-filled 3D structures using honeycomb lattice, there are two ‘Lock and Fit’ techniques to combine two individual 3D pieces. One is using the ‘Slotted cross’ shape technique and the other is using ‘Squared nut’ shape technique. For joining space-filled 3D structures using a square lattice, there is no such ‘Lock and Fit’ technique in place currently. We also didn’t come across research, which reveals a definite technique for combining two individual 3D container structures. Another challenge for us while creating a large 3D shape was the size of the scaffold. Currently, most of the DNA origami is done using the scaffold of the single stranded M13 virus. M13 scaffold has a large length of over 7000 bps and it has low secondary structure formation, which makes it the best option for DNA origami. To create larger structures, we would need multiple scaffolds since a length of 7000 base pairs would not be sufficient for the purpose. Research has been done to scale up 2D DNA origami using tiles instead of staplers, but no corresponding research work for scaling 3D structures using some kind of 3D tiles was observed.</p><br/>				
			</article>
		</li>


		<li> 
			<article>
				<header>
				<h1><a name="method">3. Methods:</a></h1>
				<p>In this section we describe both single and multiple shaped DNA origami of Taj Mahal.</p>
				
				<p style="font-size:16px;padding:20px 0 5px 0;">3.1 Single-shape DNA Origami of Taj Mahal</p> 
				</header>
				
				<p>Designing the layout, evaluating the design and determining the staple sequences of the Taj Mahal using 3D multilayer DNA origami, with a single long M13mp18 scaffold, on a honeycomb lattice is described as follows. Single-shape DNA Origami for designing the Taj Mahal using DNA origami relies on principles already established in the literature [6], and attempts to take it one step further by providing an enhanced 3D effect to the object. This design process is similar to the one used to design the 3D DNA Robot like structure, in the research published recently by Castro et al [3]. The Taj Mahal was designed while keeping in mind various stability factors, to ensure that it maintains its structure when it is self-assembles under lab conditions. We have chosen a honeycomb lattice over a square lattice for single-shape DNA origami. This is because, as stated by Castro et al in their research [3], the square lattice packing rule allows for creating densely packed objects with rectangular features but may require additional effort to eliminate potentially undesired global twist deformations. The honeycomb lattice packing rule by default create straight albeit more porous structures. Thus, we chose the honeycomb lattice for creating our structure.</p><br/>
				
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/taj_2.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/taj_2.gif"  alt="wiki-img" class="image-style">
						<p class="img-text"><b>Figure 1 </b>| The Taj Mahal, Agra, India. [24]</p>
					</a> 
				</div>
				
				<p style="font-size:14px;padding:20px 0 5px 0;">3.1.1. Procedure:</p><br/>
				
				<p>A long single stranded scaffold is used for designing the structure. The M13 scaffold was chosen for creating the Taj Mahal, because of two reasons. First is that the length of the scaffold, i.e. 7249 base pairs (bps), is sufficiently large to create the structure. Secondly, there is low secondary structure formation in the M13 Scaffold, so chances of occurrence of errors are low. As the DNA origami principle stated long ago by Paul Rothemund [18] :</p><br/>
				<p style="text-align:center">“Our goal is to choose a continuous route through the scaffold path and then generate a list of staples that would force the scaffold to adopt that configuration in the test-tube.”</p><br/>
				<p>The Taj Mahal is designed as a space-filling multilayer origami object on a honeycomb lattice. As a consequence, each double-helical domain in the lattice has up to three neighbours arranged in three-fold symmetry (Figure 2). </p><br/>
				
				<p style="font-size:14px;padding:20px 0 5px 0;">3.1.2. Crossover spacing rule:</p><br/>
				<p>A B-form DNA strand can be assumed to contain 10.5 bps per helix. Thus, this implies that the strands rotate by 240 degrees about the helical axis every 7 bps, by 480 degrees every 14 bps and two complete turns or 720 degrees every 21 bps. caDNAno also gives us the option to extend the length of the strands in the honeycomb lattice by multiples of 21 bps. In a honeycomb lattice, each strand has up to three neighbours in the honeycomb lattice. (Fig. 2)  Hence, to ensure that the DNA strands are confined to the honeycomb lattice, crossovers can be placed to each of the three neighbouring strands in constant intervals of 7 bps or every 240 degrees. It has been stated in previous research [3], that deviating from the constant 7-bp crossover spacing rule in the honeycomb-lattice packing causes local under twist as well as axial strain [4].</p><br/>
				
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/honeycomb-latice.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/honeycomb-latice.gif"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 2 </b>| Spacing in the Honeycomb lattice. Each double-helical domain can have up to three neighbouring double-helical domains.</p>
					</a> 
				</div>
								

				<p style="font-size:14px;padding:20px 0 5px 0;">3.1.3. Some more previously established designing constraints and principles:</p><br/>
				<p>Following constraints are well known from the literature:</p>
					<p>According to a recent research [9], it has been established that the DNA origami structure needs to have a crossover density to avoid the double helical domains from bowing out. It is known that a crossover density of one crossover per 7-8 base pairs, the inter-helical gap created by bowing reduces to 0.5 nm as compared to 1.5 nm for crossover density of 1 per 26 bps.</p><br/>
					<p>The staple strands can undergo multiple crossovers and connecting multiple neighbouring domains but they must obey the length constraints, i.e. the scaffold length must be between 17 to 50 bps non-inclusive [3]. Currently, caDNAno does not obey this principle in its auto-stapling feature. Thus, the staples have to be manually broken after applying auto-staple.</p><br/>
					<p>According to previous research [18,29,27], unpaired single stranded scaffold segments can be used as entropic springs to support tensegrity structures, and they are useful in preventing unwanted base-stacking interactions at object interface. Single stranded scaffold or staples can also serve as hybridization anchors for direct site attachments.</p><br/>
					<p>As stated by Castro et al in their research [3], the square lattice-packing rule allows for creating densely packed objects with rectangular features but may require additional effort to eliminate potentially undesired global twist deformations. The honeycomb lattice packing rule by default create straight albeit more porous structures. Thus, we chose the honeycomb lattice for creating our structure.</p><br/>
			
					
				<p style="font-size:14px;padding:20px 0 5px 0;">3.1.4 Basic Workflow:</p>
					<p>The Taj Mahal was structurally divided into the four pillars, the central dome and the base. Each structure was created individually using five different single scaffolds and then the pillars and the central dome were connected to the base, using scaffold crossovers. Staplers were then applied keeping the stability constraints in mind, and then the M13 sequence was installed in the scaffold and staplers.</p><br/>
					
				
				<p style="font-size:14px;padding:20px 0 5px 0;">3.1.5 Detailed Workflow:</p>
				<p>The detailed workflow is given below:</p><br/>
				
					<p>The Taj Mahal was structurally divided into the four pillars, the central dome and the base. Each structure was created individually using five different single scaffolds and then the pillars and the central dome were connected to the base, using scaffold crossovers. Staplers were then applied keeping the stability constraints in mind, and then the M13 sequence was installed in the scaffold and staplers.</p><br/>
				
					<p>A silhouette (Fig.3) of the Taj Mahal was chosen to get an idea of the dimensions of The Taj Mahal. The structure was divided into six major components, i.e. the four pillars, central dome and the base. Then these structures were further divided into grids, so that it could be designed using available CAD software for DNA origami.</p><br/>
				
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/taj-shadow.jpg" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/taj-shadow.jpg"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 3 </b>| A silhouette of the Taj Mahal, chosen for reference and understanding the dimensions of the structure.</p>
					</a> 
				</div>
				
				<p>Based on the dimensions of The Taj Mahal, there were two designing options we had to choose from, for designing the Taj Mahal. They are depicted in Fig. 4. If the entire length and width available in caDNAno for the structure was to be used, choosing the configuration in Fig.4(a) made more sense if the length and breadth of The Taj Mahal structure were considered. </p><br/>
				<p>However, since we calculated that we would not be able to use the entire space of caDNAno due to limitation on the size of the scaffold we could use, we decided to go with configuration in Fig. 4(b) for the sake of simplicity.</p><br/>
				
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/brainstorm-design.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/brainstorm-design.gif"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 4</b> | The two possible configurations which could be used for designing the Taj Mahal. Configuration (a) made more sense if the entire length and width of caDNAno was to be used. However, since a the scaffold length was limited to 7249 bps, configuration (b) was chosen for the sake of simplicity.</p>
					</a> 
				</div>

				<p>Next, 108 single stranded scaffolds in the honeycomb lattice of the Taj Mahal were chosen. The length of each of these scaffolds was chosen as 84 bps. Next the tools provided in caDNAno were used to break the scaffold at desired points to bring out specific shapes. </p><br/>
			
				<p>After this, a continuous route through all the 108 strands was chosen. This was done by installing scaffold crossovers. The task was not trivial and multiple iterations had to be made to finally join the entire structure together. The shape was compromised a bit during this process, and a few strands had to be left out, leaving 104 strands in the structure finally (Fig.5).</p><br/>

				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/scaffold-path.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/scaffold-path.gif"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 5</b> | Initially, 108 single strands were chosen for the structure. While choosing a continuous route through the scaffold, the structure had to be compromised a bit and finally a continuous route through 104 strands was chosen. The structure was made modular as it can be seen. The four pillars, and the central dome were connected to the base using scaffold crossovers.</p>
					</a> 
				</div>


				<p>After a continuous route was established, staples were installed in the structure, mostly using Auto-Staple feature provided in caDNAno, and some manually. Moreover, auto-staple feature does not generate perfect staples. The staplers had to be modified at lot of places to meet the length constraints. This was all done manually.</p><br/>
			
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/panel-2-strands.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/panel-2-strands.gif"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 6 </b>| The staplers generated to keep the 3D Taj Mahal structure stable at various levels of zoom.</p>
					</a> 
				</div>


				<p>Next, the sequence of M13 was installed into the main scaffold, and the sequence of the staplers was generated simultaneously. The Staple sequences are the extracted and copied onto a spreadsheet. The finished structure is depicted in Fig.6.</p><br/>
				
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/taj-mahal-3d.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/taj-mahal-3d.gif"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 7</b> | The 3D view taken by caDNAno panel-3 for The Taj Mahal structure finally generated by technique 1.</p>
					</a> 
				</div>
		
				<p>The staple sequence, which is thus generated, can be used to generate the Taj Mahal in lab, by using the standard methods, which are already being used [3, 26].</p><br/>
		
		
			
			<p style="font-size:14px;padding:20px 0 5px 0;">3.1.6. General information about the structure:</p>
			<p>The scaffold sequence used by to create the Taj Mahal structure is that of M13mp18. However, the entire 7249 bps of the sequence were not required, and the length of scaffold used was 6508 bps. The numbers of staplers used in the structure are 215. A .xls file of the stapler sequence that we generated and the M13mp18 sequence that we installed are available for download in the results section of the Wiki.</p><br/>
			
			<p style="font-size:14px;padding:20px 0 5px 0;">3.1.7. Calculating the dimensions of DNA Origami object:</p>
			<p>The following rules were used to calculate the dimensions of the structure:</p><br/>
			
			<p>1.	Since the space between two base pairs in a DNA strand is approximately 0.34 nm, the length of the scaffold can be calculated as 0.34 * number of (bps) in the longest strand used.</p><br/>
			
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/honeycomb.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/honeycomb.gif"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 8</b> | Calculating various dimensions of the honeycomb lattice (a) The honeycomb structure of the lattice can be represented by a hexagon. (b),(c) We know that the diameter of a DNA helix is 2 nm. Using mathematical principals, we can find out various angles and distances in the hexagon. (d),(e) The interhellical distance between two double-hellical domains placed in (d) is 4nm whereas the distance in configuration (e) is 3.46 nm (f) The height of the hexagon was calculated as 4 nm and the width is 3.46 nm.</p>
					</a> 
				</div>

			
			<p>2.	The diameter of DNA helix is 2 nm. Thus, in a honeycomb lattice, the distance various lengths and dimensions can be calculated mathematically (Fig. 8). Thus, it was calculated that the distance between two hexagonal lattices is 3.44 nm length-wise and 4 nm height-wise (Fig. 8).</p><br/>
				
				<div class="img-div">
					<a href="imgs/3d/technique_1/wiki/diagram-taj.gif" title="img" target="_blank">
						<img src="imgs/3d/technique_1/wiki/diagram-taj.gif"  alt="wiki-img" class="image-style">
						<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 9</b> | Calculating the dimensions of the Taj Mahal. The height of the pillars, h1, was calculated to be 10 nm. The height of the central dome, h2, was calculated as 12.5 nm. The base length, h4 was calculated as 28.56 nm, whereas the base width, h4 was calculated to be 39.56 nm.</p>
					</a> 
				</div>

			
			<p>According to the above calculations, the dimensions of our structure were calculated as following (Fig.9):</p><br/>
<p style="border:1px solid #ccc; padding:10px;">
				h1 = 2.5  * (honeycomb height) nm = (2.5 * 4) nm = 10 nm<br/>
				h2 = 3 * (honeycomb height) nm =  (3 * 4.828) nm = 12.5 nm<br/>
				h3 = 84 * (length of 1 bp) nm = (84 * 0.34) nm = 28.56 nm<br/>
				h4  =  11.5  * (honeycomb width) nm = (11.5 * 3.44) nm = 39.56 nm<br/>
			</p><br/>
			
			<p>Thus, the structure of the Taj Mahal was successfully created and the staplers were generated using single shape DNA origami.</p><br/>
			
		
			
			
			<p style="font-size:16px;padding:20px 0 5px 0;">3.2. Multi-shape DNA Origami</p> 
			
			<p>The Taj Mahal was successfully designed using single-shape technique, and the staplers for the structure were generated. However, the resolution of the structure was not satisfactory. A higher resolution structure was desired and so we propose multi-shaped DNA origami. </p><br/>

			<p style="font-size:14px;padding:20px 0 5px 0;">3.2.1. Stability of the structure:</p>
			<p>We wanted a higher resolution 3D model of the Taj Mahal. Since it was not possible to have a single large scaffold, which would create the whole Taj Mahal due to stability constraints and constraints on the size of the scaffold, it meant that individual pieces of the Taj Mahal which were around 7000 base pairs long would have to be created and then it was necessary to come up with a scaling technique to join these pieces to form the final structure. We also had to ensure that the technique ensured stability of the structure. There are various factors under stability that had to be considered: </p><br/>
			
			<p style="text-decoration:underline">Stability factor 1 - The base of the structure – Mechanical stability</p>
			<p>We needed a firm base for the entire Taj Mahal structure, which could hold all our individual pieces together in place, and provide mechanical stability to the structure.</p><br/>			
			
			<p style="text-decoration:underline">Stability factor 2 - Thermodynamic stability:</p>
			<p>We were also aware that the structures that we designed needed to be thermodynamically stable. We were initially not sure how to go about checking if structures are thermodynamically stable or not so we decided to do some research over this before making design decisions. </p><br/>
			
			<p style="text-decoration:underline">Stability factor 3 - Crossovers position stability:</p>
			<p>While designing the 3D structures, we decided to follow the tried and tested principles for determining the positions of the scaffold and the stapler crossovers in the structure. </p><br/>
			
			<p>We propose few techniques that showed potential in being able to scale up 3D structures. The method we followed was mainly motivated by the research done by Hao Yan group [9] recently, for designing DNA origami structures with complex curvatures in three-dimensional space. </p><br/>
			


			<p style="font-size:14px;padding:20px 0 5px 0;">3.2.2 Detailed Workflow:</p>
			<p>The detailed workflow for multi-shaped DNA origami is given below: </p><br/>
			
			<p>1. Initially, efforts were made to visualize the 3D structures using Computer Aided Designing software. A hollow sphere was created and wrapped with material assumed to be DNA, according to principles stated in Hao Yan’s research [9], just for the purpose of understanding through modeling.</p><br/>
			
			<p>2. Next some time was spent in learning and researching over Nano Engineer, which is a Bio-Molecular engineering tool for nanoscale design and simulation. All the tutorials given on the software’s website were studied and some simple 3D structures were created which could be used later in the Taj Mahal structure (Fig. 10).</p><br/>
			
			<div class="img-div">
				<a href="imgs/3d/octagon/octagonal1.png" title="img" target="_blank">
					<img src="imgs/3d/octagon/octagonal1.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 10 | (a) A Single Octagonal Ring</i></p>
				</a> 
			</div>
			
			<div class="img-div">
				<a href="imgs/3d/octagon/octagonal_cylindrical_structure.png" title="img" target="_blank">
					<img src="imgs/3d/octagon/octagonal_cylindrical_structure.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 10 | (b) An Octagonal cylinder.</i></p>
				</a> 
			</div>

			
			<p>3. Developing these structures was good for a start but we needed to focus on the bigger goal. Thus we decided to use the design principles mentioned in some of the research papers related to 3D DNA origami that we read. We built a basic pyramid using the principles we studied.</p><br/>
			
			<div class="img-div">
				<a href="imgs/3d/pyramid/pyramid1.png" title="img" target="_blank">
					<img src="imgs/3d/pyramid/pyramid1.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 11 | (a) A 3D DNA Origami Pyramid created using designing principles provided in Hao Yan’s research [9], from the Top view, </i></p>
				</a> 
			</div>

			<div class="img-div">
				<a href="imgs/3d/pyramid/pyramid2.png" title="img" target="_blank">
					<img src="imgs/3d/pyramid/pyramid2.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 11 | (b) Lateral view, and</i></p>
				</a> 
			</div>

			<div class="img-div">
				<a href="imgs/3d/pyramid/pyramid3.png" title="img" target="_blank">
					<img src="imgs/3d/pyramid/pyramid3.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 11 | (c) Top-Side view</i></p>
				</a> 
			</div>



			<p style="font-size:14px;padding:20px 0 5px 0;">3.2.3 Designing principles:</p>
			<p>There were certain factors that had to be kept in mind while designing the structure.  M13 is taken as the single stranded scaffold for designing DNA origami structures. The length of the single stranded scaffold is equal to the maximum number of base pairs that are available to form the concentric layers.  The sizes of all the must follow to the designing principles. The inner ring cannot have such a radius smaller than 3 nm, which corresponds to a minimum of 30 base-pair circumference in the innermost ring. However, for proper stability in the structure, we assumed the minimum circumference of the inner ring could be 50 nm. Each ring has been placed at a distance of 2.5 nm from its adjacent ring. This is an assumption but has been verified scientifically. Thus, the circumference of each ring depends on the adjacent ring. This is valid for the circular concentric ring structure as well as the concentric square ring structure. Scaffold crossovers should be staggered so that a single ‘seam’ is not created that could weaken the crossover network. The number of crossovers in each ring has to be a divisor of the total number of base pairs in the circumference of the ring. The DNA is quite flexible as far as the number of turns per helical turn is concerned. The deviations from around 9 bps per turn up to 12 bps per turn can be considered as stable. However, deviations larger than this are not encouraged. For a concentric ring structure, the difference between the base-pairs of two concentric rings is 50 bps, whereas for the corresponding concentric square frames structure, the difference is 60 bps. The next step was to create a master plan of the entire 3D Taj Mahal structure. The master plan prototype helped us in understanding the structure of the Taj Mahal and also gave an idea regarding the dimensions of the individual structures that would make up the Taj Mahal.</p><br/>
			

			<div class="img-div">
				<a href="imgs/3d/master-plan-final.gif" title="img" target="_blank">
					<img src="imgs/3d/master-plan-final.gif"  alt="wiki-img" style="width:600px">
					<p class="img-text"><i>Figure 12 | The master-plan of the 3D Taj Mahal</i></p>
				</a> 
			</div><br/>

			<p>Next, some basic designs were created using Nano Engineers, which used the principles that we would use later on in designing the Taj Mahal. These are Decagonal Dome (29nm radius, 10 crossovers, 8 rings), Cylindrical Tubes (10nm radius tubular), Pyramidal Tops (13nm radius, 5 crossovers, 5 rings), Cubical Body (85nm width) and a square base.</p><br/>
			
			<div class="img-div">
				<a href="imgs/3d/individual/fig3_2.png" title="img" target="_blank">
					<img src="imgs/3d/individual/fig3_2.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 13 | Individual shapes for the Taj Mahal (a) Taj Mahal pillar, in accordance with the master plan (Figure 12).</i></p>
				</a> 
			</div>

			<div class="img-div">
				<a href="imgs/3d/individual/fig3_3.png" title="img" target="_blank">
					<img src="imgs/3d/individual/fig3_3.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 13 | Individual shapes for the Taj Mahal (b) Taj Mahal dome, in accordance with the master plan (Figure 12).</i></p>
				</a> 
			</div>

			<div class="img-div">
				<a href="imgs/3d/individual/fig3_4.png" title="img" target="_blank">
					<img src="imgs/3d/individual/fig3_4.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 13 | Individual shapes for the Taj Mahal (c) Taj Mahal dome with a square body, in accordance with the master plan (Figure 12).</i></p>
				</a> 
			</div>
			
			<div class="img-div">
				<a href="imgs/3d/individual/fig3_1.png" title="img" target="_blank">
					<img src="imgs/3d/individual/fig3_1.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 13 | (d) Taj Mahal pillar and central dome with base, ararnged in space, in accordance with the master plan (Figure 12).</i></p>
				</a> 
			</div><br />

			<p>Once the individual pieces were created, the next challenge was to be able to hold these pieces together. However, we did attempt to model our thoughts using prototyping software like Autodesk Maya and Adobe Photoshop. Hence, scaling up 3D DNA origami is still a challenge for the designers. Broadly, there are two possible solutions. One is to increase the size of scaffold, which is currently around 7000 bps. However, scaffold larger than this size are difficult to synthesize. Another solution is to introduce 3D Tiles or Staplers, which can hold different individual 3D pieces together in a stable way.</p><br/>
			
			
			<h1><a name="discussions">4. Discussions:</a></h1>
			<p>We discussed a lot of designing techniques for creating 3D DNA origami nano-structures. We had chosen an ultimate goal of creating a 3D replica of The Taj Mahal as our goal.  But initially we were not sure how to go about with the designing. Simply replicating the previously used techniques was one option we had, and which is exactly what we did in single-shape DNA origami technique. However, we were not satisfied with just that. We attempted to combine the designing techniques to create a complex 3D structure and provide techniques to scale the 3D DNA origami structure. In this section we summarize our observations.</p><br/>
			
			<p style="font-size:16px;padding:20px 0 5px 0;">4.1. 3D DNA Origami with complex hollow curved surface using single M13 scaffold</p> 
			<p>This technique was motivated by a recent research by Dongran Han et al [3] where they present their research on DNA origami with complex curvatures in three-dimensional space. We felt that we could similarly create the structure of the Taj Mahal using the principles listed in the research. However, this technique failed. The reason was that the maximum size of M13 scaffold that is available for 3D DNA origami is around 7.5 – 8 thousand base-pairs in length. This number was way less than what we needed to successfully accomplish our design using this technique, which was around 35000 bps, so we had to abandon this technique too.</p><br/>
			
			<p style="font-size:16px;padding:20px 0 5px 0;">4.2 3D DNA Origami with complex hollow curved surface using single M13 scaffold for individual structures and then scaling the structure using staplers</p> 
			<p>It was proposed that first we would create individual 3D structures similar to those developed by Hao Yan et al in their research [9], using similar design principles. However, the proposed 3D structures would be a bit different in shape towards the base. Concentric rings would be provided around the base region by extending the same scaffold. Figure 14 puts forward our thoughts.</p><br/>
			
			<div class="img-div">
				<a href="imgs/3d/broad-base/broad-base2.png" title="img" target="_blank">
					<img src="imgs/3d/broad-base/broad-base2.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 14 | Illustration of the concept proposed by us, for creating 3D DNA Origami structures with an extended flattened base. </i></p>
				</a> 
			</div>

			<p>Once all these structures with a flattened extension of base are created, then a stapling technique that we proposed would come into play. We would need to apply stapler crossovers across two different scaffolds. This would be the gluing mechanism that we could use to join together two three-dimensional structures. Since all the flattened bases of all our 3D structures would lie in the same plane, we could effectively use this multiple-strand stapling technique to scale up the structures. The multiple-strand stapling using two simple 2D DNA origami objects in the same plane can be described as follows.  There would be two types of staplers in the whole structure – those that span over multiple segments of the same strand, and those that connect two strands. Figure 15 depicts our idea. </p>
			
			<div class="img-div">
				<a href="imgs/3d/broad-base/staplers-crossover-connecting-multiple-strands.png" title="img" target="_blank">
					<img src="imgs/3d/broad-base/staplers-crossover-connecting-multiple-strands.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 15 | A stapler crossover connecting two strands. The red stapler strands are used to keep the individual structures in shape, whereas the black staplers connect the two strands like a glue, by crossing over from one strand to other.</i></p>
				</a>
			</div>

			<p>As it is shown in the Figure 15 the black staplers create crossovers between two different scaffolds, and this can act as a glue to join two different strands. Similarly, we could theoretically think of joining the 3D structures with a flattened base are that we propose in a similar fashion, since we plan to keep the flattened bases of all the five structures co-planer. However, this technique requires experimental verification. </p><br/>
			
			
			<p style="font-size:16px;padding:20px 0 5px 0;">4.3 Multilayer 3D DNA Origami using space-filled structures packed on square/honeycomb lattice:</p> 
			<p>We also attempted to create the Taj Mahal using different Multilayer DNA origami space-filled structures, and looked into available techniques to join these structures together.  First of all, we created all the individual structures needed for the Taj Mahal (four pillars and central dome), and after this a master plan of the structure was created for future reference, as depicted in the figure 16.  Firstly we discussed over how the base could be created. The base could be either a single structure or it can be multiple structures holding the 3D pieces and combining the bases using 3D tile staplers. The following images (See Figures 16 and 17) illustrate both these concepts.</p><br/>
			

			<div class="img-div">
				<a href="imgs/3d/brainstorming/brainstorm1.png" title="img" target="_blank">
					<img src="imgs/3d/brainstorming/brainstorm1.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 16 | The 3D base is a single structures which holds all individual structures.</i></p>
				</a> 
			</div>

			<div class="img-div">
				<a href="imgs/3d/brainstorming/brainstorm2.png" title="img" target="_blank">
					<img src="imgs/3d/brainstorming/brainstorm2.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 17 | The 3D base can be multiple structures holding the 3D pieces and then the bases can be combined 3D tiles as staplers.</i></p>
				</a> 
			</div>

			<p>Next we discussed over how to join the five individual structures to the base. There were two options for joining the individual structures to the base.</p><br/>
			
			<p style="text-decoration:underline">1. Using slotted cross technique </p>
			<p>	Slotted cross is a standard existing technique to join two space-filled 3D multilayer origami structures. However, it involves scaffold crossovers, which means that while assigning a sequence, we treat the whole joined structure as one single scaffold. Thus this was not much useful since we were looking to scale the structure to more than one scaffold.</p><br/>
			
			<div class="img-div">
				<a href="imgs/3d/slotted-cross.jpg" title="img" target="_blank">
					<img src="imgs/3d/slotted-cross.jpg"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 18 | A slotted cross joins two 3D structures by installing a scaffold crossover.</i></p>
				</a> 
			</div><br />

			<p style="text-decoration:underline">2. Using lock and key mechanism to fit individual structures onto the base </p>
			<p>This was another proposal that was brought up. The concept is illustrated though, a two-faced tetrahedron with one of the sides intended to act as a key which would fit into a corresponding lock and fit in.</p><br/>
			
			<div class="img-div">
				<a href="imgs/3d/triangular-container.png" title="img" target="_blank">
					<img src="imgs/3d/triangular-container.png"  alt="wiki-img" class="image-style">
					<p class="img-text"><i>Figure 19 | Another joining technique proposed by us : Lock and Key technique. The bottom half of the structure can be used as a key which could fit into its corresponding lock.</i></p>
				</a> 
			</div><br />


			



			<h1><a name="koncad">5. KonCAD: DNA origami software for complex curvatures</a></h1>

				<p>While working on the project we felt that we need some kind of automation of the DNA origami process, so that we do not have to repeat the same steps over and over while starting an assignment on curved DNA origami.  This motivated us to write KonCAD, which is interactive Computer Aided Designing software focusing on prototyping, rendering and analyzing structural details of DNA origami structures with complex curvatures. The end-user needs to input the size of the structures they wish to study. For example, if the user wishes to generate or study concentric rings, they would be asked to enter the radius of the outermost ring, or if the user wishes to generate concentric square frames, they would be asked the length of the outermost frame they wish to render. Once the user provides these details, an interactive console details the analysis of the structure. The user is provided with stability details and structural details like number of base pairs in each ring, size of each ring, total number of scaffold used etc. Currently, the software supports rendering and analysis of only 2 dimensional DNA origami structures with complex curvatures. The software is hosted online <a href="avipar.xtreemhost.com/dananotrons/dacad.html" style="color:red;">here</a>.</p><br/>
			
				<p style="font-size:16px;padding:20px 0 5px 0;">5.1 Pseudo Code</p>
				<p>The pseudo code of KonCAD in programming language style is given below.</p><br/>			
				<div class="img-div">
					<a href="imgs/3d/konkad/pseudo-code.png" title="img" target="_blank">
						<img src="imgs/3d/konkad/pseudo-code.png"  alt="wiki-img" style="width:550px">
						<p class="img-text"><i>Figure 20 | The core logic of KonCAD. </i></p>
					</a>
				</div>
				


				<p style="font-size:16px;padding:20px 0 5px 0;">5.2 KonCAD Workflow Example:</p>
				<p>The following example shows the output when user inputs 30nm as the radius of the outer-most ring of the desired concentric ring structure and presses render button. First the output displayed on the console is shown in Figure 21.</p><br/>
				
				<div class="img-div">
					<a href="imgs/3d/konkad/konkad-workflow.png" title="img" target="_blank">
						<img src="imgs/3d/konkad/konkad-workflow.png"  alt="wiki-img" style="width:550px">
						<p class="img-text"><i>Figure 21 | </i></p>
					</a> 
				</div>

				
				<div class="img-div">
					<a href="imgs/3d/konkad/konkad-analysis.png" title="img" target="_blank">
						<img src="imgs/3d/konkad/konkad-analysis.png"  alt="wiki-img" class="image-style">
						<p class="img-text"><i>Figure 22 | The table which is rendered by KonCAD showing detailed analysis of each ring in the structure.</i></p>
					</a> 
				</div>
				
				<p>More details about the structure</p><br/>
				<p>The Radius of the outer-most ring that you entered is 30 nm. The Radius has been modified to 30.94 nm. The Number of rings, which can fit into the structure, is 12. The total size of scaffold used by your structure is 3900 bps. The number of base-pairs of M13 left unused is 3349 bps. </p><br/>
				
				
				<div class="img-div">
					<a href="imgs/3d/konkad/konkad-render1.png" title="img" target="_blank">
						<img src="imgs/3d/konkad/konkad-render1.png"  alt="wiki-img" class="image-style">
						<p class="img-text"><i>Figure 23 | An image dynamically rendered by KonCAD, which shows positions of scaffold crossovers.</i></p>
					</a> 
				</div>
				<div class="img-div">
					<a href="imgs/3d/konkad/konkad-render2.png" title="img" target="_blank">
						<img src="imgs/3d/konkad/konkad-render2.png"  alt="wiki-img" class="image-style">
						<p class="img-text"><i>Figure 24 |An image dynamically rendered by KonCAD, which shows positions of scaffold crossovers from a different perspective.</i></p>
					</a> 
				</div>

				<p style="font-size:16px;padding:20px 0 5px 0;">5.3. Explanation of the Example:</p>
				<p>First the software checks if the input provided by the user is a valid float or integer and other validation tests are done. After this, the software checks if the size input by the user would be able to fit into the M13 scaffold. Once the tests are successful, then it calculates the circumference of the outermost ring. Then the number of base-pairs in the outermost ring is calculated. Then the software analyses the number of base pairs in the outermost ring and tries to adjust its value to meet the stability constraints. To improve the stability of the design of the structure, the software may modify the outer radius specified by the user by +/- 1.25 nm.</p><br/>
				<p>The calculations are reinitiated using the new radius. Accordingly, the maximum number of rings possible in the structure is calculated by assuming the distance between adjacent rings to be 2.5 nm. Then a detailed analysis of each ring is provided which has all the details like ring number, base pairs in the ring, number of crossovers radius, bps/crossover and turns/crossovers bps/turn. Another adjustment that the software makes is in the base-pairs per turn. It has been shown in previous research [6] that the DNA strand is flexible with respect to the number of base-pairs per turn throughout the structure. However, this variation must not be more than 1.5 base-pairs per turn at an average. Hence our software ensures that the variation in the number of base-pairs per turn is within the accepted limits. The software then renders two images showing the structures of the generated rings from two different perspectives.  These images also display the positions of scaffold crossovers in the structure. Finally, the software displays the scaffold length used and the length of M13 left unused. It is assumed the unused length of M13 does not interfere with the remaining structure. This software is useful in the sense that the end-user would not need to worry about knowing all the designing principles for creating the structure since the structure rendered by our software already obeys all the designing principles stated in past research. Thus, a lot of time of the end-users would be saved.</p><br/>
				
				
			</article>
		</li>


		<div id="conclusion" class="box box-gray" style="padding:30px;">
			<h2 style="padding:0px 0 10px 0;">6. Conclusions</h2>
			<p>The design of the desired structure of Taj Mahal using single-shape DNA origami technique was successfully created. Keeping all the stability constraints in mind, the positioning of scaffold crossovers, stapler crossovers and the stapler sequence were determined. Joining the individual structures using Multi-shape DNA origami is still a challenge. Possible proposed solutions are to find a way to create 3D DNA Tile staplers. Another way of scaling 3D DNA origami is by increasing the size of the main scaffold (currently M13 having 7249 bps), either by joining multiple scaffolds using an enzyme such as ligase or finding an equally good but longer substitute for M13 scaffold which has low secondary structure formation. We hope in the future KonCAD software that we contribute would hopefully be extended to support 3D structures soon, and thus be even more useful as a CAD for DNA origami.</p><br/>
			</div><br /><br />


		<div id="references">
			<h1><a name="method">References</a></h1><br />

			<ul>
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			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[15] Jeanette Nangreave, Dongran Han, Yan Liu, and Hao Yan. DNA origami: a history and current perspective. Current Opinion in Chemical Biology, 14(5):608 ‚Äì 615, 2010. Nanotechnology and Miniaturization/ Mechanisms.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[16] Lulu Qian, Ying Wang, Zhao Zhang, Jian Zhao, Dun Pan, Yi Zhang, Qiang Liu, Chunhai Fan, Jun Hu, and Lin He. Analogic china map constructed by dna. Chinese Science Bulletin, 51:2973‚Äì2976, 2006.10.1007/s11434-006-2223-9.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[17] P. W. K. Rothemund. Design of DNA origami. In ICCAD ‚Äô05: Proceedings of the 2005 IEEE/ACM Internationalconference on Computer-aided design, pages 471‚Äì478, Washington, DC, USA, 2005. IEEEComputer Society.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[18] Paul W. K. Rothemund. Folding DNA to create nanoscale shapes and patterns. Nature, 440(7082):297‚Äì302, March 2006.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[19] William M. Shih and Chenxiang Lin. Knitting complex weaves with DNA origami. Current Opinion inStructural Biology, 20(3):276‚Äì282, June 2010.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[20] DNA origami may help harness solar energy. Materials Today, 9(12):65 ‚Äì 65, 2006.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[21] Jonathan Wood. The art of DNA origami: Nanotechnology. Materials Today, 9(5):9 ‚Äì 9, 2006.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[22] Zhao Zhao, Hao Yan, and Yan Liu. A Route to Scale Up DNA Origami Using DNA Tiles as Folding Staples13. Angewandte Chemie International Edition, 49(8):1414‚Äì1417, 2010.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[23] Wikipedia entry of Taj Mahal http://en.wikipedia.org/wiki/Taj_Mahal</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[24] An Image of Taj Mahal http://www.world-mysteries.com/taj-mahal-3d.jpg  </p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[25] Yonggang Ke, Jaswinder Sharma, Minghui Liu, Kasper Jahn, Yan Liu, and Hao Yan. Scaffolded DNA Origami of a DNA Tetrahedron Molecular Container. Nano Letters, 6(9):2445‚Äì2447, June 2009.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[26] Jungmann R, Liedl T, Sobey TL, Shih W, Simmel FC, Isothermal assembly of DNA origami structures using denaturing agents, J Am Chem Soc. 2008 Aug 6;130(31):10062-3. Epub 2008 Jul 10.</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[27] Tim Liedl, Bj√∂rn H√∂gberg, Jessica Tytell, Donald E. Ingber, and William M. Shih, Self-assembly of 3D prestressed tensegrity structures from DNA, Nat Nanotechnol. 2010 July; 5(7): 520‚Äì524. Published online 2010 June 20. doi:  10.1038/nnano.2010.107</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[28] Kuzuya, A. & Komiyama, M. Design and construction of a box-shaped 3D-DNA origami. Chem. Commun. (Camb.) 28, 4182-4184 (2009).</p></li>
			<li style="padding:0;border:0;margin:0;list-style-type:none;"> <p>[29] Douglas SM, Dietz H, Liedl T, H√∂gberg B, Graf F, Shih WM, Self-assembly of DNA intonanoscale three-dimensional shapesNature. 2009 May 21;459(7245):414-8.</p></li>
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